The aim of this proposal is to facilitate the understanding of radiobiological phenomena to help optimize experimental designs and to give a rigorous basis for the implementation of radiobiological knowledge to radiotherapy through the development of mathematical models and statistical methods in the fields of radiotherapy and radiobiology. Nine projects will be described, all of which involve either mathematical modeling of radiobiological phenomena or the development of the most appropriate statistical techniques for the type of data that are collected in clinical and laboratory studies of radiation response. Many of the projects involve extensive use of computers. The nine projects, arranged in three groups, are: Clinical Studies: (i) analysis of a large, meticulously collected, data set on the response of radiotherapy patients with head and neck tumors, (ii) investigation of the "shape" of dose- time curves for head and neck tumors, (iii) adaptation of some computer software to calculate biological isodoses in addition to physical isoeffective doses. Animal Experimental Studies: (iv) developing methods of analysis of late effect responses using the time to development of the effect as endpoint, (v) developing statistical methods to fit the linear-guadratic model to categorical ordered response data, (vi) design and analysis of top- up experiments, (vii) developing statistical methods for analyzing hair depigmentation data as an example for a general model for this type of radiobiological data, (viii) developing statistical methods for the analysis of overdispersed data in radiobiology. Experimental and Clinical Correlations: (ix) development of a mathematical model for regeneration in acutely-responding tissues. There is a wide spectrum of problems in radiation research which are amenable to mathematical approaches and a number of other projects are in various stages of development. The mathematical models will be developed and tested on a variety of data sets available to the investigators. Equally important, we have the facilities to apply the results of such modeling to experimental testing.